Optical fibers are used to carry information and energy by the transmission of light. However, when light of a high power is guided by a conventional optical fiber, nonlinear effects, such as Raman and Brillouin scattering, occur in the fiber. These nonlinear effects cause a reduction in the power transmitted, or reduce the quality of the signal used for carrying information in the fiber. To increase the power handling capability, an optical fiber having a guiding region with increased cross-section has been developed. This reduces the optical power density in the fiber thereby reducing non-linear effects. An example of an optical fiber having increased cross-section is a large mode area fiber (LMAF).
High power lasers are used in the field of materials processing. To achieve an output beam of high enough quality for this application, the optical fiber used to transmit the beam is preferably single mode. LMAFs having single mode operation are difficult to attain using conventional refractive index fiber guiding design techniques because as the core diameter increases to provide the large core area, the refractive index difference between the core and the cladding must decrease. For example, for a fiber having a core diameter of 35 μm and a cutoff wavelength of 1.3 μm, the refractive index difference must be about 0.02% for single mode operation. However, it is difficult to obtain such a small refractive index difference in silica based glass using existing doping techniques, such as, adding to the core a material to increase the refractive index, or adding to the cladding a material to decrease the refractive index.
If the fiber cannot be designed to be truly single mode, it is possible to design fibers that provide single mode operation even though they support cladding modes to a small degree. Such fibers may be made by considering the amount of coupling from the core mode to cladding modes and the degree of loss of the cladding mode. If the amount of coupling is small, and the degree of loss is high, then the fiber may work efficiently as a single mode fiber because any transfer of the light intensity to the cladding modes will be rapidly damped thereby preventing degradation of the output beam.
Large mode area photonic crystal fiber (LMAPCF) has been proposed to provide a fiber with a large core to reduce the power density in the fiber and reduce non-linear effects. LMAPCF is made of a single type of glass material and doping is unnecessary. The required refractive index difference between core and cladding is defined by the size of air holes formed in the cladding. Practical LMAPCFs have been developed having a core diameter of 35 μm for use at a wavelength of 1.55 μm, 25 μm for use at 1.06 μm, and 20 μm for use at 0.8 μm. If the core diameter becomes larger than these values, perhaps by decreasing the diameter of the air-holes in the cladding, the bend loss of the air-hole type LMAPCF becomes large which is undesirable. A problem with LMAPCFs is that they are difficult to manufacture. For example, it is difficult to accurately control the size of the air holes as the fiber is drawn. Furthermore, LMAPCF has a higher transmission loss compared to optical fibers without air holes.
Alternatively, large mode area fiber can be realized using an all-solid photonic bandgap fiber (PBGF) design. All-solid PBGFs do not have air holes and hence have lower transmission loss. Furthermore, the PBGF can be manufactured using conventional fiber production methods and apparatus.
For example, a conventional all-solid PBGF having a periodic structure consisting of an array of step index rods is shown in FIGS. 2a and 2b. FIG. 2a shows the refractive index profile of a high index rod. The high index rod has a diameter d. FIG. 2b shows the periodic arrangement of the high index rods in the cladding of the all-solid PBGF. In FIG. 2b, a parallelogram (shown as a dashed line) shows a unit cell of the two dimensional periodic structure. The distance from the centre of one high index rod to an adjacent high index rod is Λ. The diameter of the core may be considered to be 2Λ-d, where the core is made by removing single high index rod from the periodic structure.
FIG. 1 shows the relationship between core diameter for an all-solid photonic bandgap fiber, and normalized frequency kΛ of operation. As the core diameter or the ratio d/Λ becomes larger, the normalized frequency kΛ becomes larger (where k represents free space wave number, i.e. 2π/wavelength).
A problem with the resulting conventional PBGF is that it has discrete transmission spectra which restrict the practical wavelength range of operation. Additionally, close to the edges of the transmission band, confinement loss and bend loss are high which further reduce the useable wavelength range. Furthermore, the bend loss is high at even order transmission bands when the parameter d/Λ is around 0.4 (as mentioned above d represents the diameter of a high index region in the periodic structure of the cladding, and Λ represents the pitch of the periodic structure of the cladding). However, for single mode operation in conventional all-solid PBGF in which the high index periodic structure is an array of rods, the parameter d/Λ must be small, so the operational wavelength range of the conventional all-solid PBGF large mode area fiber is small.
FIGS. 3a to 3d are graphs showing a photonic density of states produced by the periodic structure of the cladding. The density of states was calculated using the method described in “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell's equations in photonic crystals”, Phys. Rev. B 71, 195108 (2005). In the figures, the abscissa represents normalized frequency kΛ, and the ordinate represents effective refractive index, neff. FIGS. 3a to 3d show the density of states for values of the parameter d/Λ of 0.2, 0.4, 0.6, and 0.7 respectively. In the calculation, the refractive index of the background is 1.45, and the refractive index of the high-index rod is 1.48, thereby providing a refractive index difference of around 2%.
FIGS. 4a to 4d show a calculated density of states for the same values of d/Λ. In these figures, the abscissa again represents normalized frequency kΛ, whereas the ordinate is changed to represent the parameter (β2-n2k2)Λ2 which represents a modal parameter of the electromagnetic field. In particular, (β2-n2k2)Λ2 is an eigenvalue of the scalar wave equation for photonic crystal microstructures. This modal parameter is described in more detail in “Scaling laws and vector effects in bandgap-guiding fibres”, Optics Express Vol. 12, 69-74 (2004). Parameters n and β represent the background index of the cladding and longitudinal component of wave vector respectively.
In the graphs of FIGS. 4a to 4d, the plain dark areas represent bandgaps where the density of states is zero. The gray scale areas represent the existence of cladding modes, that is, modes that exist solely or partly in the cladding. The number of cladding modes increases as the grey scale changes from dark to light.
FIGS. 3a to 3d show that at lower values of the normalized frequency kΛ, the bandgaps become deeper (along the ordinate) and narrower (along the abscissa). Qualitatively, the depth of the bandgap (along the ordinate) corresponds to bend loss of the fiber. As the depth becomes shallower (i.e. smaller refractive index difference between allowed modes), the bend loss increases.
As shown in FIGS. 3a to 3d, the bandgaps between cladding modes also become deeper and narrower as the parameter d/Λ becomes larger.
In FIG. 3b, a core guided mode has been superposed on to the cladding modes, and is shown by a thin white line. This core guided mode is calculated for the case in which a single high index rod is removed from the periodic structure. The core guided mode is shown with a normalized frequency from 23 to 60, and bandgap edges at normalized frequencies of 37, 40, and 60.
As mentioned above, FIGS. 4a to 4d show the modal parameter (β2-n2k2)Λ2 of the cladding modes against normalized frequency kΛ. As the bandgaps become deeper, the difference in the modal parameter between the core guided modes and the cladding modes which form the bottom of the bandgap increases which results in core guided modes with a well confined electromagnetic field in the core region of the fiber. This also results in an increased number of core guided modes. Core guided modes have been calculated for kΛ=100 and are represented by data points in FIGS. 4a to 4d. In FIGS. 4a and 4b, only one core mode lies in the bandgap, and so the optical fiber operates in single-mode. FIGS. 4c and 4d show more than one core mode. In these cases the data point at the largest modal parameter, that is closest to zero, represents the fundamental core guided mode, and the data point at the next largest modal parameter is the first high-order mode. As seen from the figures, when the parameter d/Λ is no greater than 0.4 (FIGS. 4a and 4b), the optical fiber operates in single mode.
From FIGS. 3a to 3d and 4a to 4d it is evident that there is a trade off between bend loss and the maximum core diameter (or smallest wavelength) capable of supporting single mode operation. This is similar to normal index guiding optical fibres, but is exacerbated in PBGF because the trade-off requires even narrower design tolerances. In a PBGF with d/Λ set to about 0.4 to provide single mode operation, a transmission band is largely limited by the bend loss and the bend loss becomes large in even order bandgaps and around the edges in every bandgap. This is caused by the wavelength dependence of the bandgap depth which is inevitable for conventional PBGF.